Table Of ContentPrinciples of Quantum
Mechanics
SECOND EDITION
R. Shankar
Yale University
New Haven, Connecticut
PLENUM PRESS • NEW YORK AND LONDON
Library of Congress Cataloging-in-Publication Data
Shankar, Ramamurti.
Principles of quantum mechanics I R. Shankar. --2nd ed.
p. em.
Includes bibliographical references and index.
ISBN 0-306-44790-8
1. Quantum theory. I. Title.
QC174. 12.S52 1994
530.1'2--dc20 94-26837
CIP
ISBN 0-306-44790-8
©1994, 1980 Plenum Press, New York
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No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any
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Printed in the United States of America
To
My Parents
and to
Uma, Umesh, Ajeet, Meera, and Maya
Preface to the Second Edition
Over the decade and a half since I wrote the first edition, nothing has altered my
belief in the soundness of the overall approach taken here. This is based on the
response of teachers, students, and my own occasional rereading of the book. I was
generally quite happy with the book, although there were portions where I felt I
could have done better and portions which bothered me by their absence. I welcome
this opportunity to rectify all that.
Apart from small improvements scattered over the text, there are three major
changes. First, I have rewritten a big chunk of the mathematical introduction in
Chapter I. Next, I have added a discussion of time-reversal invariance. I don't know
how it got left out the first time-! wish I could go back and change it. The most
important change concerns the inclusion of Chaper 21, "Path Integrals: Part II."
The first edition already revealed my partiality for this subject by having a chapter
devoted to it, which was quite unusual in those days. In this one, I have cast off all
restraint and gone all out to discuss many kinds of path integrals and their uses.
Whereas in Chapter 8 the path integral recipe was simply given, here I start by
deriving it. I derive the configuration space integral (the usual Feynman integral),
phase space integral, and (oscillator) coherent state integral. I discuss two applica
tions: the derivation and application of the Berry phase and a study of the lowest
Landau level with an eye on the quantum Hall effect. The relevance of these topics
is unquestionable. This is followed by a section of imaginary time path integrals
its description of tunneling, instantons, and symmetry breaking, and its relation to
classical and quantum statistical mechanics. An introduction is given to the transfer
matrix. Then I discuss spin coherent state path integrals and path integrals for
fermions. These were thought to be topics too advanced for a book like this, but I
believe this is no longer true. These concepts are extensively used and it seemed a
good idea to provide the students who had the wisdom to buy this book with a head
start.
How are instructors to deal with this extra chapter given the time constraints?
I suggest omitting some material from the earlier chapters. (No one I know, myself
included, covers the whole book while teaching any fixed group of students.) A
realistic option is for the instructor to teach part of Chapter 21 and assign the rest
as reading material, as topics for a take-home exams, term papers, etc. To ignore it, vii
viii I think, would be to lose a wonderful opportunity to expose the student to ideas
that are central to many current research topics and to deny them the attendant
PREFACE TO THE
excitement. Since the aim of this chapter is to guide students toward more frontline
SECOND EDITION
topics, it is more concise than the rest of the book. Students are also expected to
consult the references given at the end of the chapter.
Over the years, I have received some very useful feedback and I thank all those
students and teachers who took the time to do so. I thank Howard Haber for a
discussion of the Born approximation; Harsh Mathur and Ady Stern for discussions
of the Berry phase; Alan Chodos, Steve Girvin, Ilya Gruzberg, Martin Gutzwiller,
Ganpathy Murthy, Charlie Sommerfeld, and Senthil Todari for many useful com
ments on Chapter 21. I thank Amelia McNamara of Plenum for urging me to write
this edition and Plenum for its years of friendly and warm cooperation. Finally, I
thank my wife Uma for shielding me as usual from real life so I could work on this
edition, and my battery of kids (revised and expanded since the previous edition)
for continually charging me up.
R. Shankar
New Haven, Connecticut
